Question 10 of 51beginner🔧 ApplyNumerical2 marks

Find the 10th10^{th} and 15th15^{th} terms of the sequence tn=5n−3t_n = 5n - 3 for n≥1n \geq 1.

Correct Answer

Given: The nthn^{th} term of the sequence is given by the formula tn=5n−3t_n = 5n - 3 for n≥1n \geq 1.

Calculation for 10th10^{th} term: To find the 10th10^{th} term, we substitute n=10n = 10 into the given formula.

t10=5(10)−3t_{10} = 5(10) - 3 t10=50−3t_{10} = 50 - 3 t10=47t_{10} = 47

Calculation for 15th15^{th} term: To find the 15th15^{th} term, we substitute n=15n = 15 into the given formula.

t15=5(15)−3t_{15} = 5(15) - 3 t15=75−3t_{15} = 75 - 3 t15=72t_{15} = 72
Exercise: Exercise Set 8.1 | Q: 2 | (Page 6)
For More Understanding

Explanation

The question requires evaluating the explicit formula for the nth term of a sequence at specific values of n. By substituting n=10 and n=15 into the formula t_n = 5n - 3, we directly calculate the 10th and 15th terms respectively.

Solution Steps

  1. Step 1: Substitute n = 10 into t_n = 5n - 3, giving t_10 = 5(10) - 3 = 50 - 3 = 47.

  2. Step 2: Substitute n = 15 into t_n = 5n - 3, giving t_15 = 5(15) - 3 = 75 - 3 = 72.

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